Question

A wire can be broken by applying load of $200N$. The force required to break another wire of the same length and same material, but double in diameter is

• A. $200N$
• B. $400N$
• C. $600N$
• D. $800N$

Answer 1

The correct option is D $800N$

Since the wires have same material, their modulus of elasticity must be same.

Thus, the ratio of longitudinal stress to longitudinal strain (which is Young's Modulus of Elasticity) must be same. Now, before breaking, the strains in both wires must be the same too.

Therefore, stress $=$ Young's modulus $\times$ strain, must be same for both wires.

The second wire has diameter double that of the first wire, so area of cross section of second wire is 4 times as large as that of first wire. Therefore, to develop the same stress, the force applied on second wire must be 4 times as large as the force applied on the first wire (since stress = force/cross section area).

Thus, force that needs to be applied to second wire to break it is $4\times 200=800N$